The Complex Networks community has been exposed to this approach – and makes by now use of it – via the notion of Gromov hyperbolicity, itself stemming from Gromov's seminal work on hyperbolic groups [1]}.
The – perhaps somewhat theoretical in the eyes of many practitioners – notion above is connected to the notion of network backbone, underlying the long-distance relations between major network regions. Indeed, the connection between negative curvature and these “communication highways" in networks has been emphasized in [2]}.
